基于偏正态数据下联合位置与尺度混合专家回归模型的参数估计
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摘要
混合专家回归模型广泛应用于异质总体数据的分类,聚类及回归分析中.研究基于偏正态数据,提出了联合位置与尺度混合专家回归模型,该模型同时对位置,尺度和混合比例参数建模,应用MM算法和EM算法研究了该模型参数的极大似然估计.通过随机模拟和实例分析说明了该模型和方法的有效性与实用性.
The mixture of expert regression models are widely used for classification of heterogeneous data, clustering and regression analysis. Based on the skew-normal data, the mixture expert regression models for joint location and scale are proposed, which is used to simultaneously model the location, scale and mixture proportion parameters of interest. MM algorithm and EM algorithm are considered to estimate unknown parameters in the maximum likelihood estimation procedure. Monte Carlo simulation and a real data are used to verify the proposed method.
The mixture of expert regression models are widely used for classification of heterogeneous data, clustering and regression analysis. Based on the skew-normal data, the mixture expert regression models for joint location and scale are proposed, which is used to simultaneously model the location, scale and mixture proportion parameters of interest. MM algorithm and EM algorithm are considered to estimate unknown parameters in the maximum likelihood estimation procedure. Monte Carlo simulation and a real data are used to verify the proposed method.
引文
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[4]万文,吴刘仓,马梦蝶.偏正态数据下联合位置与尺度模型的统计诊断[J].应用数学,2017,30(2):313-321.
[5]马婷,吴刘仓,黄丽.基于偏正态分布联合位置、尺度与偏度模型的极大似然估计[J].数理统计与管理,2013,32(3):433-439.
[6]朱志娥,吴刘仓,戴琳.偏t正态数据下混合线性联合位置与尺度模型的参数估计[J].高校应用数学学报,2016,31(4):379-389.
[7]Jacobs R A,Jordan M I,Nowlan S J,et al.Adaptive mixtures of local experts[J].Neural Computation,1991,3(1):79-87.
[8]Yuksel S E,Wilson J N,Gader P D,et al.Twenty years of mixture of experts[J].IEEE Transactions on Neural Networks,2012,23(8):1177-1193.
[9]Chamroukhi F.Skew-normal mixture of experts[A].International Joint Conference on Neural Networks[C].IEEE,2017,3000-3007.
[10]Chamroukhi F.Robust mixture of experts modeling using the t distribution[J].Neural Networks,2016,79:20-36.
[11]Zeller C B,Cabral C R,Lachos V H,et al.Robust mixture regression modeling based on scale mixtures of skew-normal distributions[J].Test,2015,25(2):375-396.
[12]Titterington D M,Smith A F M,Markov U E.Statistical Analysis of Finite Mixture Distributions[M].New York:Wiley,1985.
[13]Nguyen H D,Mclachlan G J.Laplace mixture of linear experts[J].Computational Statistics and Data Analysis,2016,93:177-191.
[14]Mclachlan G.Finite mixture models[J].Partha Deb,2000,39(4):521-541.
[2]Park R E.Estimation with heteroscedastic error terms[J].Econometrica,1966,34(4):888.
[3]Aitkin M.Modelling variance heterogeneity in normal regression using GLLM[J].Applied Statistic,1987,36(3):332-339.
[4]万文,吴刘仓,马梦蝶.偏正态数据下联合位置与尺度模型的统计诊断[J].应用数学,2017,30(2):313-321.
[5]马婷,吴刘仓,黄丽.基于偏正态分布联合位置、尺度与偏度模型的极大似然估计[J].数理统计与管理,2013,32(3):433-439.
[6]朱志娥,吴刘仓,戴琳.偏t正态数据下混合线性联合位置与尺度模型的参数估计[J].高校应用数学学报,2016,31(4):379-389.
[7]Jacobs R A,Jordan M I,Nowlan S J,et al.Adaptive mixtures of local experts[J].Neural Computation,1991,3(1):79-87.
[8]Yuksel S E,Wilson J N,Gader P D,et al.Twenty years of mixture of experts[J].IEEE Transactions on Neural Networks,2012,23(8):1177-1193.
[9]Chamroukhi F.Skew-normal mixture of experts[A].International Joint Conference on Neural Networks[C].IEEE,2017,3000-3007.
[10]Chamroukhi F.Robust mixture of experts modeling using the t distribution[J].Neural Networks,2016,79:20-36.
[11]Zeller C B,Cabral C R,Lachos V H,et al.Robust mixture regression modeling based on scale mixtures of skew-normal distributions[J].Test,2015,25(2):375-396.
[12]Titterington D M,Smith A F M,Markov U E.Statistical Analysis of Finite Mixture Distributions[M].New York:Wiley,1985.
[13]Nguyen H D,Mclachlan G J.Laplace mixture of linear experts[J].Computational Statistics and Data Analysis,2016,93:177-191.
[14]Mclachlan G.Finite mixture models[J].Partha Deb,2000,39(4):521-541.